Drawing
Little Vasya loves to draw.
Today, he has a table with N rows and M columns and wants to paint its cells in various colors. To make the coloring less predictable, he follows this method:
For each row i from 1 to N, Vasya paints all the cells in the i-th row red with a probability of R_i%.
For each column j from 1 to M, Vasya paints all the cells in the j-th column blue with a probability of C_j%.
If a cell is painted both red and blue, it becomes green due to the mixing of colors.
Initially, none of the cells in the table are painted. After Vasya completes his process, G cells end up being green. Your task is to determine the expected total number of cells that Vasya paints in any color (red, blue, or green).
Input
The first line of the input contains three integers N, M, and G, separated by spaces.
The second line contains the integers R_1, R_2, ..., R_N, separated by spaces.
The third line contains the integers C_1, C_2, ..., C_M, separated by spaces.
All numbers in the input are integers. 1 ≤ N, M ≤ 100, 0 < R_i, C_i < 100, 0 ≤ G ≤ N·M.
There is at least one way to paint some rows red and some columns blue such that exactly G cells become green.
Output
Output the expected total number of painted cells. The absolute error of the output should not exceed 10^{-5}.